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Innovation and Adoption of Electronic Business Technologies
Kai Sülzle
Ifo Working Paper No. 38
December 2006
An electronic version of the paper may be downloaded from the Ifo website www.ifo.de.
Ifo Working Paper No. 38
Innovation and Adoption of Electronic Business Technologies*
Abstract This paper presents a duopoly model of e-business technology adoption. A leader and a follower benefit from a new e-business technology with uncertain quality depending on its innovation and adoption cost and both firms’ adoption timing. When innovation and adoption require large set-up costs, the leader favors quick adoption by the follower. The follower prefers either late or no adoption. This is due to a delayed first-mover benefit which stems from an innovators’ capability to impose a new technology stan-dard. It is shown that inter-firm adoption subsidies are a viable tool to quicken adoption. JEL Code: O31, L1. Keywords: Electronic business, adoption, innovation, network effects.
Kai Sülzle Ifo Institute for Economic Research
at the University of Munich and Dresden University of Technology
Poschingerstr. 5 80539 Munich, Germany
Phone: +49(0)89/9224-1282 [email protected]
* The author thanks participants of the annual conference of the Verein für Socialpolitik 2006, Bayreuth, the EARIE 2006, Amsterdam and the Conference on the Economics of Information and Communication Technologies 2006, Paris for helpful comments. Further thanks go to Tom Kiessl and Thomas Fuchs for helpful remarks.
1 Introduction
The timing and nature of new technology adoption are fundamental issues of
firms’ business performance. In particular in the last decade, innovation and
adoption of electronic business (e-business in the following) technologies, such
as procurement platforms or collaborative product development tools played a
crucial role as innovative enabler for professional activities and relationships.
The decision to adopt an e-business innovation is an investment decision
that involves costs in the expectation of future rather than immediate rewards
which are based on efficiency gains in firms’ production activities. Since firms
are usually in competitive and/or collaborative situations, their gains from an
innovation crucially depend on the behavior of other firms.
For example in the automotive industry, large automobile manufacturers
and their core suppliers decide on the implementation of electronically en-
abled tools for collaborative product development, e.g. DaimlerChrysler and
Bosch who use collaborative CAD tools for the design and integration of head-
light components in cars. Another example for such an e-business technol-
ogy are procurement platforms as SupplyOn in the automotive industry or
click2procure.com by Siemens.1
Particularly in the innovation and adoption process of e-business technolo-
gies, pioneering firms usually receive low returns from technology use as long
as they are the single users of the new technology. The reasoning for this obser-
vation is twofold: First, technology leaders incur R&D costs in the innovation
and implementation phase while the quality of the innovation might still be
uncertain. Second, since the innovator of an e-business technology introduces a
new technology standard, due to network effects, the earlier other firms adopt
the higher might an innovator benefit of an applied technology.
In contrast, followers might not want to adopt quickly since they face lower
implementation and adoption costs when they wait longer, i.e. until the quality
of the innovation is revealed. Followers might even not adopt at all because
they do not want to commit to an external standard developed by another
firm.
1The author and his colleagues have conducted 40 interviews on the usage, adoptionand implementation of e-business technologies with CEOs from major industry players toelectronic platform providers and suppliers in France, Italy and Germany.
1
These incentive structures and profit expectations result in two observa-
tions: First, new technologies are never adopted by all potential users simul-
taneously.2 Second, the adoption decision crucially depends on the amount of
improvement which the new technology offers over any previous technology, its
costs of development and implementation and the adoption decision of related
firms.
In this context the present paper contributes to the technology adoption
literature by accounting for the described peculiarities of e-business technol-
ogy adoption. In a duopolistic setup we analyze the incentives for innovation
and adoption timing of an innovator and an adopter and determine the corre-
sponding cost ranges where the new e-business technology is applied.
Related Literature: While there are many industry-specific and innovation-
specific case studies of the adoption of new technologies, the theoretical liter-
ature on the adoption of electronic business activities is sparse. Hoppe (2002)
and Geroski (2000) provide excellent surveys on both the theoretical literature
on new technology adoption and patent races.
Most theoretical contributions have a common base in the seminal work
by Reinganum (1981), who provides a duopoly model of technology adoption.
In her model a change in market concentration may speed or slow technol-
ogy adoption if firms make once-and-for-all commitments to their eventual
adoption dates. Fudenberg and Tirole (1985) extend this work by studying
situations in which firms decide at any point in time whether to adopt a cost-
reducing new technology, knowing that adoption costs decline over time. By
assumption, the increase in profits due to innovation is greater for the first
follower than for the second. This potential first-mover advantage stimulates
preemption up to a point where the extra profit flow for the first mover just
equals the extra costs of speeding up adoption.
Gotz (1993) analyzes the adoption and diffusion of a new technology in a
market for a differentiated product with monopolistic competition, showing a
positive relationship between firm size and speed of adoption. Additionally, he
2See e.g. Gotz (1993).
2
identifies a rank effect, stating that potential users differ with respect to the
(expected) returns from adoption. Further, a stock effect implies a dependency
of firms’ adoption payoffs on the stock of firms already using a new technology.
Such stock effects imply an asymmetry in payoffs of adoptions, which give rise
to differing rather than uniform adoption dates in both market and planner
solutions.
One of the first contributions dealing with technology adoption in the
presence of network externalities was offered Katz and Shapiro (1986). They
studied the dynamics of industry evolution in a market with technological
change where two inherently incompatible technologies are subject to network
externalities. They show that a potential second-mover advantage may result
in subgame-perfect equilibria without preemption and payoff equalization. In
their model, payoffs to different firms are asymmetric. They further state that
in such a setup, network effects are a crucial feature. They dispose over two
fundamental effects: first, the relative attractiveness today of rival technologies
is influenced by their sales histories: a given product is more attractive the
larger is the in-place base of consumers using that product. Second, in the
presence of network externalities, a consumer in the market today also cares
about the future success of the competing products.
The most related contribution is Benoit (1985), which is based on Jensen
(1982), who introduced uncertainty of the profitability of an innovation into
the adoption and diffusion literature. In a duopoly model Benoit (1985) derives
that a technology leader’s expected profits from innovation are not monotonic
in the cost of innovation, given that successful innovation is probabilistic. He
further shows that an increase in the innovation cost may cause followers to
adopt the innovation. In contrast to his contribution we will show that a
technology leader profits from early adoption of a follower, while the follower
prefers to wait. A viable tool to overcome this discrepancy of interest is the
application of inter-firm adoption subsidies.
A similar result where a monopolist may benefit by giving away a technol-
ogy to a competitor after a time lag, is derived by Farrell and Galliani (1988).
3
In their model a monopolist benefits from delayed adoption by a competitor
because of a price commitment effect on a downstream consumer market. In
contrast to the present contribution there is no driving force to induce accel-
erated adoption due to an inherent network effect in their model.
The remainder of the paper is structured as follows: Section 2 introduces
the e-business model. Section 3 analyzes its equilibrium outcome. In section 4
we discuss the possibility of inter-firm innovation cost subsidies as an extension.
Section 5 provides a numerical calibration exercise and section 6 concludes the
paper.
2 The Model
The basic framework is a modified version of the duopoly model by Benoit
(1985), which is adjusted to e-business technology adoption. Consider two risk-
neutral and profit maximizing firms using the current best-practice technology
which decide upon innovation and adoption of a new e-business technology.
The two firms are not necessarily competitors but could also be vertically
related players in a value chain or industry. The adoption decision depends on
the expected benefits from using the new technology, its implementation cost
and the adoption behavior of the other firm.3
The first firm, which will be labeled L as leader, has the know-how and
resources for the innovation of a new e-business technology. It faces the decision
of whether to innovate and implement the new technology or not. When L
chooses to develop the new technology, it incurs a fixed cost C(≥ 0)4 and
the new technology will be implemented N(≥ 0) periods after the innovation
decision.
The second firm is labeled F as follower. F gets informed about L’s inno-
vation decision only when the e-business technology is implemented, which is
N periods after L’s investment. The follower then has the following possibil-
3Note, this paper focusses exclusively on the costs and benefits associated with the inno-vation and adoption of a new technology. An analysis of a downstream product or customermarket is not an issue.
4Although it is theoretically possible that C < 0, we do not consider this case since itwould not lead to qualitatively different results.
4
ities of technology adoption: (1) never adopt the new technology; (2) match
the new e-business technology immediately at a cost5 C with an implemen-
tation lag N or (3) decide to wait for K periods until the quality of the new
technology is revealed. In this case, F will adopt the new technology only if
it is a success and not a failure.6 There is no loss of generality through the
assumption that L is the first firm to decide upon innovation. If L did not
innovate, after some time, F would independently have the same innovation
possibilities and hence perform the same calculations as L.
The initial benefit of technology use when both firms apply the old tech-
nology is normalized to 0. During any single period in which L has innovated
but not (yet) F , the leader earns ΠL(1, X) and F earns ΠF (1, X). The first
argument in brackets shows that only one firm uses the technology. Let X be a
random variable that can take one of two values: with probability p it takes the
value xs (for “e-business technology is a success”) and with probability (1−p) it
takes the value xf (for “e-business technology is a failure”). If both firms have
implemented the new e-business technology, L earns ΠL(2, X) while F earns
ΠF (1, X).7 Both firms are risk-neutral and maximize the expected present
values of their profits with the discount rate δ ∈ (0; 1).
The relative magnitudes of the respective per period profits from technol-
ogy usage are supposed to be as specified in the following assumption.
Assumption 1 The relative magnitudes of the per period profits from elec-
tronic business technology usage for both firms are:
Leader Follower
ΠL(1, xs) > ΠL(1, xf ) ΠF (2, xs) > ΠF (1, xs)
ΠL(2, xs) > 0 ΠF (2, xs) > ΠF (2, xf )
ΠL(1, xs) < ΠL(2, xs) ΠF (1, xs) ≤ ΠF (1, xf )
5We assume that the cost F for technology innovation and adoption are the same for bothfirms. This could be justified in terms that L has higher costs for product development whileF incurs higher implementation costs for staff training for example, since the technology isnot produced inhouse.
6Obviously, it makes no sense to wait longer than K periods if the new e-business tech-nology is a success. Also, it does not pay to wait any period if a bad innovation will also bematched.
7As Benoit (1985) we do not specify the process from which these payoffs arise sincethere is no need to do so. The only requirement is that this process is relatively stable, sothat when innovation and adoption occurs, the situation changes in a predictable way.
5
Before considering fixed costs, the leader prefers a successful innovation to a
failed innovation. Further, L prefers a successful innovation where both firms
apply the new technology to no innovation. Due to network effects of e-business
technologies, L is better off if both firms use the e-business technology when
it is a success than if L is the single user.
If the new e-business technology is a success, F is better off adopting than
not matching the new technology (before considering fixed costs). If F also
adopts, it is better off when the new technology is a success than a failure.
When F does not adopt, it is better off if the innovation is a failure than if it
is a success.
Once a firm has implemented the new technology, there is no way to reverse
this decision, i.e. the firm stays with the new technology in any case.8 It
is further assumed that the true quality of the new e-business technology is
not revealed immediately after its implementation but K(≤ N) periods after
the first firm innovated. Before these K periods, the firms receive no new
information on X.
Accordingly, let ΠL(1, X) and ΠF (1, X) denote the single period profits
before the end of the K periods.
By backwards induction, we determine the subgame perfect equilibrium
of the game where L decides upon innovation or not and F decides upon its
response. In this regard, the leader L has to build an expectation about the
follower’s response when deciding whether to innovate or not. It is assumed
that L correctly assesses F ’s beliefs about the innovation of the e-business
technology. The notation for present values of the corresponding payoffs are
depicted in Table 1 below. We only depict those present values for the case
that (at least) L innovates. If no firm innovates and adopts the new technology
we assume that both firms use the old technology with a normalized per period
profit equal to zero.
8This means that the added cost of reversing the investment is prohibitive.
6
Follower
never adopt waitadopt immediately K periods
V Fn V F
a V Fk
Leader innovate V Ln V L
a V Lk
Table 1: Notation and allocation of present values
The following analysis of the model builds on the mutual best responses of
the two firms, based on the respective present values, associated with their
decision to innovate and adopt or not. Applying backwards induction, we first
analyze the follower’s decision problem.
2.1 The Follower’s Decision Problem
Given that L innovates and implements the new e-business technology, the
follower F has three choices: (1) never adopt the new technology, (2) wait
for K periods with the adoption decision adopt, or (3) adopt immediately. In
the latter case, F immediately incurs a fixed cost C and the new technology
will be implemented after N periods. If F waits for K periods, it can observe
whether the innovation is successful or not and then adopts if it is.
2.1.1 Expected present value when F never adopts
If F decides to never respond to an innovation by L, the present value of this
strategy is given by:
V Fn ≡
K−1∑i=0
δiE[ΠF (1, X)
]+
∞∑i=K
δiE[ΠF (1, X)
], (1)
where E[ ] is the expected value operator. During the first K periods after
the implementation of the new e-business technology by L, F receives the
expected single period payoff E[ΠF (1, X)
]while L uses the new technology
alone. After K periods, both firms learn the realization of X, but since F did
(and does) not adopt, the follower receives the expected single period payoff
ΠF (1, X) in every subsequent period.
7
2.1.2 Present value when F adopts immediately
If F adopts immediately after having noticed that L has innovated (i.e. N
periods after L’s innovation decision), F expects the present value:
V Fa ≡ −C +
K−1∑i=0
δiE[ΠF (1, X)
]+
N−1∑i=K
δiE[ΠF (1, X)
]+
∞∑i=N
δiE[ΠF (2, X)
]. (2)
The fixed cost C has to be incurred immediately with the decision to adopt.
Again, during the first K periods after the implementation of the new
e-business technology by L, F receives the expected single period payoff
E[ΠF (1, X)
]and L uses the new technology alone. After K periods, both
firms learn the type of X, and F receives the expected payoff single period pay-
off ΠF (1, X) until F ’s new e-business technology is also implemented (which
happens N periods after F ’s adoption decision). Afterwards, when both firms
apply the new technology, F receives the payoff ΠF (2, X) in every period that
follows (see Figure 1 for an illustration of the time structure in this case, where
t denotes the time periods).
Figure 1: Timing, when F adopts immediately
2.1.3 Present value when F waits K periods till adoption decision
Finally, F can choose to wait K periods (until the type of X is revealed) and
then adopt (or not in case that the innovation is a failure). The present value
of this strategy is given by:
V Fk ≡
K−1∑i=0
δiE[ΠF (1, X)
]+ (1− p)
∞∑i=K
δiΠF (1, xf )
+p
(−δKC +
N+K−1∑i=K
δiΠF (1, xs) +∞∑
i=N+K
δiΠF (2, xs)
). (3)
8
Again, F receives the expected single period payoff E[ΠF (1, X)
]in the first K
periods after the implementation by L. Then, if the new technology is a failure,
which happens with probability (1− p), F does not adopt the new technology
and hence receives ΠF (1, xf ) in every following period. Otherwise, if the new
technology is a success, F chooses to adopt and incurs the present value of the
fixed costs F . Further, F receives ΠF (1, xs) as long as the implementation of
the new technology did not yet occur. After the implementation F receives
ΠF (2, xs) in all future periods (see Figure 2 below).
Figure 2: Timing, when F waits for K periods with adoption decision
2.1.4 The follower’s adoption choice
The follower’s choice depends upon which of the above expressions is the great-
est. It will never respond, if:9
C >δN
1− δ
(ΠF (2, xs)− ΠF (1, xs)
)≡ C (4)
The argument in (4) describes F ’s incentive to adopt to a successful innova-
tion. Given that the innovation is successful, F will only adopt if at least
the discounted additional per period benefit ΠF (2, xs) − ΠF (1, xs) from new
technology usage, which begins N period after F ’s potential adoption decision,
is higher than its adoption cost C. Otherwise, F will decide to never adopt
the new technology. Hence, if (4) does not hold, F will wait K periods, if
9See the appendix for a derivation of this relationship.
9
V Fk > V F
a which is the case, when10
(1− pδK)C >δN
1− δE[ΠF (2, X)− ΠF (1, X)
]−δK+N
1− δp(ΠF (2, xs)− ΠF (1, xs)
)≡ (1− pδK)C. (5)
Contrarily, if (5) does not hold, the follower prefers to adopt immediately. The
following proposition summarizes the follower’s choice, which depends on these
crucial values of the fixed technology adoption cost C.
Proposition 1 Ceteris paribus, depending on the fixed adoption cost C, the
follower’s adoption choice can be specified as follows:
For C ∈
(0, C], then F adopts immediately,
(C, C], then F waits K periods with its adoption decision,
(C,∞], then F never adopts.
Proof. The follower’s respective preferences of thee possible actions follow
from (4) and (5). It remains to show that C ≤ C. This holds when
E[ΠF (2, X)− ΠF (1, X)
]≤ ΠF (2, xs)− ΠF (1, xs) , (6)
which is the case for all p ∈ [0; 1]. �
The intuition of Proposition 1 is that, all other things remaining unchanged,
the higher the fixed adoption cost C, the more likely the follower will either
delay its adoption decision until the quality of the new technology is revealed
or even not adopt at all.
10Again, see the appendix for this condition.
10
2.2 The Leader’s Decision Problem
Given the choice by the follower, the leader has to choose between developing
and implementing the e-business technology or not. When calculating the
respective present values from innovation, L takes into account conditions (4)
and (5), so for each of the three possible responses by F , L decides whether
to innovate or not.
2.2.1 L’s present value from innovation if F never adopts
If F never adopts, L will innovate, if the present value from innovation V Ln is
positive, yielding
V Ln ≡ −C +
N+K−1∑i=N
δiE[ΠL (1, X)
]+
∞∑i=N+K
δiE[ΠL (1, X)
]> 0. (7)
When L innovates and F never adopts, F incurs fixed costs C and receives
the expected single period payoff E[ΠL(1, X)
]until the type of X is revealed
(which happens after N+K periods). Afterwards, L is the only user of the new
technology and receives E [ΠL (1, X)] in every subsequent period. Let Cn be
the corresponding crucial fixed cost value which determines if the innovation
provides a positive present value. From (7) it follows that this is the case if
C <δN+K
1− δE[ΠL (1, X)
]+
δN − δN+K
1− δE[ΠL (1, X)
]≡ Cn. (8)
If C < Cn then L will innovate if F ’s response is to never adopt the new
e-business technology.
2.2.2 L’s present value from innovation if F adopts immediately
Given that F chooses the strategy to adopt immediately, L will innovate if
V La > 0, which reads as
V La ≡ −C +
N+K−1∑i=N
δiE[ΠL (1, X)
]+
2 N−1∑i=N+K
δiE[ΠL (1, X)
]+
∞∑i=2 N
δiE[ΠL (2, X)
]> 0 (9)
11
Again, if L innovates, it incurs fixed costs C. In the time interval between the
point in time when the new e-business is implemented and the realization of X
is revealed (in N + K), the leader receives E[ΠL(1, X)
]per period. Between
the revelation of X and the implementation of the new technology at F , L is
the only user of the new technology and hence receives the per period payoff
E [ΠL (1, X)]. Figure 3 shows the timing from L’s perspective.
Figure 3: Timing when F adopts immediately
In this case (9) determines the crucial fixed cost threshold value Ca for L’s
innovation decision as
C <δN − δN+K
1− δE[ΠL (1, X)
]+
δN+K − δ2N
1− δE[ΠL (1, X)
]+
δ2N
1− δE[ΠL (2, X)
]≡ Ca. (10)
If C lies below Ca then L will innovate if F ’s response is to adopt immediately
after having noticed that F had innovated.
2.2.3 L’s present value from innovation if F waits K periods to
adopt
If F chooses to wait K periods till it adopts, L will innovate, if V Lk > 0:
V Lk ≡ −C +
N+K−1∑i=N
δiE[ΠL (1, X)
]+ (1− p)
∞∑i=N+K
δiΠL (1, xf )
+p
(2 N+K−1∑i=N+K
δiΠL (1, xs) +∞∑
i=2 N+K
δiΠL (2, xs)
)> 0. (11)
The intuition for the payoff till period N + K is identical to the case when F
adopts immediately. Since F now waits K periods to decide whether to adopt
12
or not, F will learn which X-type the technology provides. Accordingly, if X
is of type xf , F will not adopt and therefore L receives the per period payoff
ΠL (1, xf ) in all future periods. With probability p the new technology is a
success. Then F adopts and L subsequently receives the per period payoff∑2 N+K−1i=N+K δiΠL (1, xs) +
∑∞i=2 N+K δiΠL (2, xs) . (See Figure 4 for a graphical
illustration of the timing.) Now, the corresponding crucial fixed cost value Ck
Figure 4: L’s timing when F waits for K periods with its adoption decision
is determined by (11) as
C <δN − δN+K
1− δE[ΠL (1, X)
]+ p
δN+K − δ2N+K
1− δΠL(1, xs)
+pδ2N+K
1− δΠL (2, xs) + (1− p)
δN+K
1− δΠL(1, xf ) ≡ Ck. (12)
Again, if C lies below this threshold value, L will innovate if F ’s response is
to wait for K periods.
From the determination of the respective present values from L’s innova-
tion decision, it is easy to see that L is better off when the follower never
adopts than when the follower waits K periods, if V Ln > V L
k , which is the case
when
δN+K
1− δE[ΠL (1, X)
]> p
δN+K − δ2N+K
1− δΠL(1, xs) + p
δ2N+K
1− δΠ1 (2, xs)
+(1− p)δN+K
1− δΠL(1, xf ),
which reduces to
0 > pδ2N+K
1− δ
(Π1(2, xs)− Π1(1, xs)
). (13)
13
This inequality never holds since per assumption Π1(2, xs) > Π1(1, xs). Obvi-
ously, L is better off if the follower plays the strategy of waiting than of never
adopting, because a beneficial usage of the new e-business technology requires
both firms to apply the new technology.
Accordingly, L prefers F to adopt immediately compared to having F wait
for K periods, if V La > V L
k , which holds when
0 > p(1− δK)(ΠL (1, xs)− ΠL (2, xs)
)+ (1− p)
(ΠL (1, xf )− ΠL (2, xf )
).(14)
From assumption 1 we know that ΠL(1, xs) < ΠL(2, xs). Further, if
ΠL (1, xf ) ≤ ΠL (2, xf ) then (14) holds for any p ∈ (0; 1]. Otherwise, if
ΠL (1, xf ) > ΠL (2, xf ) such that L would be worse off if both firms use the
new technology when it is a failure than if L were the single user of the new
technology, then (14) holds only if
p >ΠL (2, xf )− ΠL (1, xf )(
ΠL (1, xs)− ΠL (2, xs))(1− δK) + ΠL (2, xf )− ΠL (1, xf )
≡ J. (15)
It is easy to see that J ∈ (0; 1). Hence, p would have to be sufficiently large
so that (14) holds. The assumption that p is sufficiently large can be justified
by the intuition that the new e-business technology will only be innovated and
implemented if the prospects of success are high. The following proposition
summarizes the leader’s preferences.
Proposition 2 Ceteris paribus, for a given C the technology leader’s expected
present value from innovation is higher when the follower also adopts the new
e-business technology, compared to the strategy when the follower never adopts.
When the probability p for a successful innovation is high, i.e. p > J , the
leader prefers the follower to adopt immediately. If p ≤ J the leader prefers
the follower to adopt immediately only if ΠL (1, xf ) ≤ ΠL (2, xf ).
Otherwise, if ΠL (1, xf ) > ΠL (2, xf ) the leader prefers the adopter to wait
with its adoption decision until the type of the new e-business technology is
revealed.
Proof. The proof of the first part of Proposition 2 follows from (13) and
the second part from (14) and (15). �
14
The intuition for the crucial value J is as follows: when the probability for
a successful innovation is high, L wants F to follow quickly, since L benefits
from the jointly used new technology more than in case of a failure and in case
that L is the single user. Practically this could be that F imposes a certain
standard of the new technology, which benefits L when F also adopts to this
technology, since L would not have any further adjustment cost. When the
probability for a successful innovation is low, L prefers F to wait, since the
possible beneficial network effect from the joint usage of the new technology
vanishes in case of a failure.
3 Equilibrium in the e-Business Model
The above approach completely characterizes the conditions for innovation
and adoption, together with the respective resulting benefits from technology
usage. In order to determine the resulting equilibrium outcome of the game,
the leader’s and follower’s respective crucial innovation cost values for each of
the follower’s three adoption options have to be compared. For simplicity, in
the following we make the assumption that11
ΠL (1, X) = ΠL (1, X) . (16)
Accordingly, it follows that (8) now provides
Cn =δN
1− δE[ΠL (1, X)
], (17)
and (10) reduces to
Ca =δN − δ2N
1− δE[ΠL (1, X)
]+
δ2N
1− δE[ΠL (2, X)
]. (18)
Due to (16) and (12), it holds that
Ck =δN
1− δE[ΠL (1, X)
]+ p
δ2N+K
1− δ
(ΠL(2, xs)− ΠL(1, xs)
). (19)
From (17), (18) and (19) it follows immediately that Ck > Cn and Ca > Cn.
The relationship between Ck and Ca depends on p as specified in (15):
11See Benoit (1985) for this assumption.
15
• For ΠL (1, xf ) < ΠL (2, xf ), it holds that Ca > Ck, whereas
• for ΠL (1, xf ) ≥ ΠL (2, xf ), it holds that Ca ≥ Ck if p ≥ J and Ca < Ck
if p < J .
In the context of e-business technology adoption, the relevant case is
ΠL (1, xf ) < ΠL (2, xf ). The intuition is that the leader is worse off if it is
the single user of the new technology, compared to the situation when both
firms apply the new technology given that it is a failure. This is because if
we consider F and L to be participants in an R&D consortium, they cannot
interact if on firm (L) uses the new technology and the other firm (F ) uses the
old technology. When both firms apply the new technology, then there could
be some interaction, although it would have been better if both still used the
old technology, given that the new technology is a failure.
Therefore, consider the case where ΠL (1, xf ) < ΠL (2, xf ) such that
Ca > Ck(> Cn).12 The leader’s and follower’s best responses stem from the
comparison of their respective crucial cost values which depend on the relative
magnitudes of
E[ΠL (1, X)
]+ pδN+K
(ΠL(2, xs)− ΠL(1, xs)
)≡ Q, (20)
E[ΠL (1, X)
]≡ R, and (21)
ΠF (2, xs)− ΠF (1, xs) ≡ S. (22)
Q is the leader’s expected single period benefit when the follower waits K
periods with its adoption decision. This expected benefit is decomposed into
the safe benefit E[ΠL (1, X)
]that L receives in every period after the new
technology is implemented and a discounted mark-up which L receives only
if F adopts after K periods to a successful innovation, which happens with
probability p. Accordingly, R is the leader’s expected single period benefit
when the follower never adopts. S is the followers gain in its single period
benefit from adopting to a successful innovation. It obviously holds that Q ≥ R
and hence
Ck > Cn. (23)
12The same analysis applies to the case of ΠL (1, xf ) ≥ ΠL (2, xf ) when p > J .
16
Depending upon the specific parameter values, four innovation and adoption
patterns can be distinguished: L innovates and F either adopts immediately,
waits for K periods or never adopts. Furthermore, a situation where no in-
novation takes places can be an equilibrium result. The following proposition
summarizes these outcomes.
Proposition 3 Two types of equilibrium outcomes can be distinguished:
1. If the new technology is such that L has more to gain than F when F
adopts a successful innovation, i.e. Q ≥ S, then
L innovates and F adopts immediately
L innovates and F waits K periods
L innovates and F never adopts
no innovation occurs
if C ∈
(0, C],
(C, C],
(C, Cn], for R > S,
(max{C, Cn},∞).
2. Otherwise, if the new technology is such that L has less to gain than F
when F adopts a successful innovation, i.e. Q < S, then
L innovates and F adopts immediately
L innovates and F waits K periods
no innovation occurs
if C ∈
(0,min{Ca, C}],(C, Ck], for C < Ck,(max
{Ck,min{Ca, C}
},∞).
Proof. The proof of the first part of Proposition 3 looks at the case when
Q ≥ S. When also S ≥ R, then it follows that Ck > C > Cn. The allocation
of L’s and F ’s respective cost threshold values is then as illustrated in Figure
5 below. Note that in this situation it does not matter whether Cn ≤ C or
Cn < C since Cn < C in any case. The resulting equilibrium outcome then
depends on the innovation and adoption cost C in the following way:
For C ∈
(0, C], L innovates, and F adopts immediately,
(C, C], then L innovates, and F waits K periods,
(C,∞], then no innovation occurs.
In this case, F is the crucial player for the determination innovation and
adoption occurs or not.
If instead of S ≥ R it holds that S < R then Ck > Cn > C. In this case the
17
Figure 5: Distribution of crucial C-values for Q ≥ S ≥ R
Figure 6: Distribution of crucial C-values for Q ≥ R > S
crucial threshold values for the innovation and adoption cost are as in Figure
6. Again, L innovates and F adopts immediately, if C ≤ C and L innovates
and F waits for K periods with its adoption decision, if C ∈ (C, C]. Now,
L can afford to innovate and be the single user of the new technology for
C-values in the interval (C; Cn]. If C > Cn, no innovation takes place.
The second part of Proposition 3 considers the case where S > Q(> R), such
that C > Ck > Cn. In this case, two sub-cases with regard to the relative
levels of C and Ck have to be distinguished:
1. When
0 ≥ E[Π2(2, X)− Π2(1, X)
]− δKP
(Π2 (2, xs)− Π2 (1, xs)
)−(1− PδK)
(E[Π1 (1, X)
]− PδN+K
(Π1(1, xs)− Π1(2, xs)
))≡ G, (24)
18
then it follows that Ck ≥ C. Hence it holds that
for C ∈
(0, C], L innovates, and F adopts immediately,
(C, Ck], L innovates, and F waits K periods,
(Ck,∞), no innovation occurs.
Accordingly, one of the two following graphically illustrated outcomes
evolves. Note that there is no qualitative difference in the two potential
Figure 7: Possible distributions of crucial C-values for C > Ck > C
outcomes. Whether Ca ≶ C depends on whether
(1− δN)E[Π1 (1, X)
]+ δNE
[Π1 (2, X)
]≶ Π2 (2, xs)− Π2 (1, xs) . (25)
2. Contrarily, when (24) does not hold and therefore G > 0, it follows, that
Ck < C. In this case, the following equilibrium outcome evolves:
For C ∈
(0, min{Ca, C}] then L innovates, and F adopts immediately,
(min{Ca, C},∞] then no innovation occurs.
Figure 8: Possible distributions of crucial C-values for C > Ck
19
The upper threshold cost value for which innovation occurs at least is
determined by the minimum of Ca and C. This minimum is C, when
0 ≥ E[ΠF (2, X)− ΠF (1, X)
]− (1− δN)E[ΠL (1, X)]− δNE[ΠL (2, X)]
−pδK[ΠF (2, xS)− ΠF (1, xs)− E[ΠL (1, X)] + δNE[ΠL (1, X)]
−δNE[ΠL (2, X)]]≡ M. (26)
Otherwise, if M > 0 then Ca < C and hence innovation only occurs for
C-values lower than Ca. Both possible cases are illustrated in the Figure
8 above. �
The assumptions underlying the outcome in case 2 of Proposition 3 are not
very likely to apply for innovation of an e-business technology. This is because
usually a pioneering firm counts with higher expected returns from innovation
than adopters which is counterintuitive to the case of S > Q.
In the more appropriate case for the innovation of an e-business technology
as in part 1 of Proposition 3, no innovation occurs for C > C. The follower’s
incentive structure is crucial to determining whether innovation occurs or not
and whether F immediately adopts or delays the adoption decision. One ex-
ample for such a delayed adoption is the case of click2procure.com which is a
procurement platform provided by Siemens. Initially, this platform was exclu-
sively used by Siemens. Only recently, after some experience on the quality of
the new technology, also external corporations use the platform for procure-
ment purposes. Hence, Siemens as innovator now benefits from the adoption
of other firms to their technology.
Proposition 4 With high innovation and adoption costs for the e-business
technology and M < 0, the followers reluctance to adopt immediately or its
general refusal to adopt, hinders innovation.
Proof. For Q ≥ S (which implies M < 0), no innovation occurs for C > C.
In this situation L would obviously like to innovate for
C ∈
(max{C, Cn}, Ck], if F would wait K periods,
(Ck, Ca], if F would adopt immediately.
20
For Q < S and M < 0, no innovation occurs for C > max{C, Ck}, but L
would innovate if F would adopt immediately, for C ∈ (max{C, Ck}, Ca]. �
Note that only for M ≥ 0, and therefore Ca < C, no innovation occurs
because L does not innovate, although F would adopt to an innovation. In
this case, no innovation occurs for C > Ca, but since then Ca < C, the follower
would have an incentive to adopt immediately for C ∈ {Ca, C}. As already
mentioned above, this scenario is not very appropriate to innovation of an
e-business technology.
Hence, the non-adoption decision of the follower prevents the leader from
innovating, although the leader would expect positive returns if the follower
were to adopt. Such an outcome is typical for an e-business technology in-
novation decision: due to network effects the more or the earlier other firms
adopt, the higher is the benefit of an applied technology to its innovator since
the first innovator sets the technology standard. Firms that invest in the de-
velopment of such technologies impose a new standard and therefore crucially
depend on the adoption behavior of customers, suppliers and even competi-
tors. Additionally, pioneering firms usually face lower payoffs from technology
use during the time of implementation when they are the only user of the new
e-business technology.
4 Extension: Inter-firm Subsidies
The above results show that both firms adopt the new technology only if
the e-business innovation and adoption costs C are low enough. When C is
higher than the specified threshold values, either no firm innovates and adopts
the new technology or just L innovates and F either postpones the adoption
decision until the quality of the innovation is revealed or even never adopts.
Accordingly, when C is within the ranges specified in Proposition 3, only
one firm might have an incentive to innovate or adopt, which results in no
innovation. Except in the case of R > S, innovation occurs for C ∈ (C, Cn]
and L is the single user of the new technology. Otherwise, the lack of adoption
hinders innovation. A viable tool to overcome this shortfall is the application
21
of inter-firm adoption subsidies. Examples for such subsidies are software
installation, staff schooling or consulting services. Let β be such an inter-firm
payment that reduces its beneficiary’s innovation and adoption cost C and
increases the corresponding cost of its payer. in order to induce innovation with
immediate or delayed innovation, β has to fulfill the following requirements at
a given C:
1. The present value from innovation or adoption of the payer of the subsidy
β must be weakly higher when the payer’s innovation cost C is increased
by β than the present value at an innovation cost C.
2. The present value from innovation or adoption of the receiver of the
subsidy β must be weakly higher than in the case of not receiving the
subsidy. Further, when L subsidizes F then C−β must be lower than C
(or C) to induce immediate (or delayed) adoption. When F subsidizes
L then C − β must be lower than Ca (or Ck) to induce innovation with
immediate (or delayed) adoption.
Therefore, when firms can subsidize each other, the following result holds.
Proposition 5 The application of inter-firm adoption subsidies can either en-
able innovation which otherwise would not have occurred or quicken adoption.
When Q ≥ S then L can benefit from innovating and subsidizing F to
induce immediate adoption for C ∈(C, min{C+Ca−Ck,
C+Ca
2}]
and a delayed
adoption decision by F for C ∈(max
{C, min{C + Ca − Ck,
C+Ca
2}}
, C+Ck
2
].
When Q < S and M ≤ 0, then L can benefit from innovating and subsi-
dizing F to induce immediate adoption for C ∈ (C, min{C + Ca−Ck,C+Ca
2}].
For C ∈(min{Ck, min
{C + Ca − Ck,
C+Ca
2
}, C+Ck
2
], F can subsidize L to
induce innovation with potential delayed adoption after K periods.
Otherwise, if M > 0, F can subsidize L to induce innovation with immediate
adoption for C ∈ (Ca,C+Ca
2] and innovation with potential delayed adoption
for C ∈ ( C+Ca
2, C+Ck
2].
Proof. When Q ≥ S then Ck ≥ C which also implies Ca > C. Accordingly,
in a situation where F does not adopt immediately, i.e. C > C, in order to
22
induce innovation with immediate adoption by the follower, β would have to
be such that for the leader it holds that
V La (C + β) ≥
V L
k (C), if C ∈ (C, C]
V Ln (C), if G > 0 ∧ C ∈ (C, Cn]
0, if C > max{Cn, C}
∧ C + β ≤ Ca, (27)
and for the follower
C − β ≤ C. (28)
It follows a β can fulfills the second part of (27) and (28) only for
C ≤ C + Ca
2. (29)
With a given C higher than C+Ca
2, L would have to pay such a high subsidy
β to induce F ’s immediate adoption to an innovation, that C + β would be
higher than Ca. Hence, this increase in L’s cost due to the high β prevents L
from innovating although F would adopt.
From the definition of V La , V L
k and V Ln in (7), (9) and (11) it follows that
in this case the first part of (27) and (28) only hold for
C ≤ C + Ca − Ck. (30)
Since both conditions (29) and (30) have to hold simultaneously, the mini-
mum of these two values determines the highest C-value, up to which F can
subsidize L to induce innovation with immediate adoption.
When C > min{C + Ca − Ck,C+Ca
2} such that L cannot induce imme-
diate adoption by subsidizing F , L can still innovate and achieve that F
makes its adoption decision after K periods instead of never adopting. In this
case β has to be such that
V Lk (C + β) ≥
V Ln (C), if G > 0 ∧ C ∈ (C, Cn]
0, if C > max{Cn, C}
∧ C + β ≤ Ck. (31)
Additionally, for the follower it must hold
C − β ≤ C. (32)
23
Due a similar argumentation as above, this is only possible for
C ≤ C + Ck
2. (33)
The second part of Proposition 5 considers the case Q < S implying Ck < C.
Hence, L might only induce immediate but not delayed adoption through a
subsidy. This happens for M ≥ 0, under the same conditions as derived above
for the case of Q ≥ S. Further, when M ≥ 0 then a subsidy from F to L could
induce innovation with potential delayed adoption. In this case β would have
to be such that
C − β ≤ Ck ∧ C + β ≤ C. (34)
Obviously, those conditions only hold simultaneously for C < C+Ck
2so that for
C ∈ (Ck,C+Ck
2], F can subsidize L to induce innovation with potential delayed
adoption after K periods.13
Finally, when M < 0, it holds that Ca < C such that only F can apply
an innovation subsidy to L to induce innovation, when C > Ca. To induce
innovation with immediate adoption, β would have to be such that
C + β ≤ C ∧ C − β ≤ Ca. (35)
To induce innovation with a delayed adoption decision, β would have to be
such that
C + β ≤ C ∧ C − β ≤ Ck. (36)
The conditions under which those respective requirements hold are specified
above. Hence, now F pays the subsidy to induce innovation for a C in the
specified ranges as in the last part of Proposition 5. �
As determined in Proposition 2, L prefers F to adopt quickly rather than
to wait with its adoption decision or even not to adopt at all. This is due
13Note, that in this case, if Ck < min{C + Ca − Ck, C+Ca
2 }, L could adopt F to induce
immediate adoption an F could subsidize L to induce innovation with delayed adoption, for
C ∈ (min{C + Ca − Ck, C+Ca
2 }, C+Ck
2 ]. Both firms prefer the case when L subsidizes F .
24
to the standard setting capability of a pioneering firm, which implies a posi-
tive network effect that benefits L when F adopts to its standard. For high
C-values the payment of an inter-firm adoption subsidy is a viable tool to
enable or at least quicken innovation and adoption, that would otherwise not
have happened. Therefore, in e-business relationships, pioneering firms often
sponsor or subsidize the adoption by suppliers, customers and even competi-
tors in terms of staff training, consulting or even financial support for new
hard- and software investments. Such a situation corresponds to the first part
of Proposition 5. But also the other case as described in the second part of
Proposition 5, where followers pay subsidies to pioneering firms are observable
in the e-business practice. For example in customer-supplier relationships, the
introduction of electronic procurement platforms by large companies such as
Siemens with click2procure.com put high pressure on its suppliers. Therefore
suppliers had to adopt to the new standard since otherwise they would have
lost the customer. Besides the application of explicit registration fees, such an
implicit cost can also be interpreted as a type of subsidy. The present paper
does not specify the decision process that determines which player pays the
subsidy and how big it is. Accordingly, the outcome of the second part of
Proposition 5 does not imply that F necessarily induces the payment. It could
also be that L offers F a contract that commits F to make a payment as in
the mentioned examples.
25
5 Calibration Excercise
In order to shed some light on the rather technical approach above, consider
the following numerical example. Many different combinations of parameter
values are possible under the setup in Assumption 1. The following calibration
exercise provides an example for each of the two equilibrium types of Q ≥ S
and Q < S, as derived in Proposition 3.
Scenario 1
Assume that the respective magnitudes of the per period profits from electronic
business technology usage for both firms take the following values:
Leader Follower
ΠL(1, xs) = −0.500 ΠF (1, xs) = −0.000ΠL(1, xf ) = −0.800 ΠF (1, xf ) = −0.100ΠL(2, xs) = −2.000 ΠF (2, xs) = −0.300ΠL(2, xf ) = −0.500 ΠF (2, xf ) = −0.200
Note that the assumption of a positive ΠF (1, xf ) could be justified by the
intuition that the follower gets a small positive benefit when it does not match
a failed innovation. This could be interpreted as an ideological benefit from not
making the same “mistake” as the leader or by thinking of an expectation of
any future advantage when the follower possibly introduces a new technology
and hence builds on the experience from having a bad example in terms of the
leader’s failed innovation.
Certainly, if we think of an old technology that already disposes of some
network effects, then ΠF (1, xf ) and ΠF (1, xs) would have to be negative. Since
the per period benefits when both firms use the old technology is normalized
to zero, the present model does not consider this option.
Given the per period benefits from above, we get the calculated values:
E[ΠL(1, X)] = 0.240 Q = 0.396 Cn = 0.130E[ΠL(2, X)] = 1.500 R = 0.240 Ca = 0.277E[ΠF (1, X)] = 0.020 S = 0.300 Ck = 0.214E[ΠF (2, X)] = 0.200 M = −0.230 C = 0.037
G = −0.170 C = 0.162
26
Since Q > S > R, it holds that Ck > C > Cn such that this scenario is an
example for the first part of Proposition 3. The corresponding alignment of
the crucial values for C is as depicted in Figure 5 above.
The equilibrium outcome is then as follows: For C < C = 0.037 innovation
with immediate adoption occurs . For C ∈ (C = 0.037, C = 0.162] L innovates
and F waits for K periods with its adoption decision. This is because Q > S,
which implies Ck > C. For C > C = 0.162, no innovation occurs because of
S > R and therefore Cn < C .
Figure 9 plots the corresponding present values (PVs) for different C-
values, given the per period benefits from technology usage as in Scenario 1.
See the appendix for the underlying data table. The straight lines show the
Figure 9: Present values for the case Q > S > R as in Scenario 1
leader’s expected present values from innovation and the dotted lines are the
follower’s respective expected values from adoption. The result from Proposi-
27
tion 2 that for any given C the leader prefers immediate adoption to delayed
adoption and delayed adoption to no adoption is obvious. Furthermore, in the
cost-intervall (0, C], immediate adoption provides the highest expected present
value for F . From the intersection of V Fa and V F
k at C until C, the best option
for F is to wait for K periods with its adoption decision. For higher C-values
than C, no adoption is best for F . Since there is no uncertainty associated
with the decision to never adopt, V Fn is constant.
The intersections of the zero line with L’s expected present values from
innovation, given the three choices by F , determine the leaders crucial values
Cn, Ck and Ca, respectively.
As stated in Proposition 5, adoption subsidies could induce earlier in-
novation. Given the exemplary numbers, L could innovate and subsidize
F ’s immediate adoption for C ∈(C, C + Ca − Ck
]= (0.037, 0.100] since
C+Ca
2= 0.157 > C+Ca−Ck = 0.100. Due to C = 0.162 > C+Ca−Ck = 0.100,
L could subsidize F for C ∈ (C, C+Ck
2] = (0.162, 0.188], to enable innovation
with potential delayed adoption by F .
Such a subsidy could work as follows:
• Consider innovation and adoption costs C ′ = 0.050. With such costs,
L innovates and F waits for K periods, providing V Lk (C ′) = 0.164 and
V Fk (C ′) = 0.104, respectively.14
L could subsidize F with a β = 0.025 such that F ’s adoption cost would
be reduced to C ′ − β = 0.050 − 0.025 = 0.025 which is lower than
C = 0.037. Accordingly, L’s innovation costs increase to C ′ +β = 0.075,
which is still lower than C + Ca − Ck = 0.100.
After the application of the subsidy, innovation with immediate adoption
occurs, providing V La (C ′ + β) = 0.202 > V L
k (C ′) = 0.164 and V Fa (C ′ −
β) = 0.122 > V Fk (C ′) = 0.104. Hence, the application of the subsidy
quickens adoption as derived in Proposition 5.
14See the appendix for the calculated data.
28
• Consider innovation and adoption costs C ′′ = 0.175. At this costs, no
innovation occurs, because C ′′ > C, providing benefits equal to 0 for
both firms.
Here, L could subsidize F with a β = 0.010 such that F ’s adoption cost
would be reduced to C ′′−β = 0.170− 0.010 = 0.160 which is lower than
C = 0.162. L’s innovation costs increase to C ′′ + β = 0.180, which is
lower than C+Ck
2] = 0.188.
Applying the subsidy enables innovation with a delayed adoption decision
by F , providing V Lk (C ′′ + β) = 0.034 > 0 and V F
k (C ′′ − β) = 0.051 > 0.
Hence, both firms are better off with the subsidy which enables innova-
tion.
Scenario 2
Now that ΠF (2, xs) = 0.800 (instead of 0.300 as in Scenario 1), while all
other things remain unchanged as in Scenario 1. Accordingly, we now get the
following calculated values:
E[ΠL(1, X)] = 0.240 Q = 0.396 Cn = 0.130
E[ΠL(2, X)] = 1.500 R = 0.240 Ca = 0.277
E[ΠF (1, X)] = 0.020 S = 0.800 Ck = 0.214
E[ΠF (2, X)] = 0.600 M = −0.070 C = 0.204
G = −0.010 C = 0.432
Obviously, S > Q > R and therefore C > Ck > Cn so that this is an example
for the second part of Proposition 3 (and also 5).
Now, the following equilibrium outcome evolves: for C < C L innovates
and F adopts immediately; for C ∈ (C, Ck] L innovates and F waits for
K periods to decide whether to adopt or not; for C > Ck no innovation
occurs. The corresponding present values are plotted in Figure 10.15 Following
Proposition 5, for C ∈ (C, min{C + Ca − Ck,C+Ca
2}] L could subsidize F to
15The description of the crucial values in the plot follows the intuition as in Scenario 1
and is selfexplaining. See the data table in the appendix.
29
Figure 10: Possible distributions of C-values for the case C > C > Ck
induce innovation with immediate adoption. Since C + Ca − Ck = 0.267 >
C+Ca
2= 0.240, this applies for C ∈ (0.204, 0.240]. Following the argumentation
as in Scenario 1 above, the exemplary values C = 0.230 and β = 0.030 provide
such an outcome.
For C ∈(min{Ck, min
{C + Ca − Ck,
C+Ca
2
}, C+Ck
2
]= (0.240, 0.323], a
subsidy from F to L enables innovation with a delayed adoption decision.
Take a given C = 0.260 and the subsidy β = 0.050, for example.
30
6 Conclusion
The present paper accounts for the specifics of the innovation and adoption
process of electronic business technologies that are determined by the amount
of fixed costs for development and implementation of a new technology. When
the adoption of an e-business technology requires large set-up costs, a firm’s
decision to adopt or not depends on the comparison of gains and losses, asso-
ciated with the use and installation of the new technology.16
Particularly in the adoption process of e-business technologies, followers
benefit from late adoption since they face lower R&D costs for the develop-
ment of an e-business software, for example. Due to this peculiarity, pioneering
firms usually face lower payoffs from technology use during the time of imple-
mentation. Further, such leaders in e-business adoption scenarios usually have
lower benefits from technology usage when they are the only user of a new
e-business technology. This is due to network effects, the more or the earlier
other firms adopt, the higher is the benefit of an applied technology to its
innovator due to the fact that the first innovator sets the technology standard.
An additional focus of the analysis is on the commonly observable subsidiza-
tion activities of firms that develop and apply e-business technologies, because
they benefit indirectly from the adoption of related business partners, as in a
customer supplier relationship, for example.
The current model could be extended in various ways: one obvious ex-
tension could be the analysis in an oligopolistic setup instead of the 2-firm
case. Nonetheless, the results deduced above contain some predictive power
for such a scenario as well. An innovator of a new technology would still have
standard setting capacities associated with fixed development costs. But in an
oligopolistic scenario, it could be the case that the network effect that results
from an increase in the number of adopting firms somehow has an upper ceil-
ing in terms of the total number of followers if we think of potential network
congestion in terms of administrative and service costs.
Another interesting extension would be to endogenously determine the
16See Chen (1996).
31
number of periods the follower would optimally choose to adopt as well as
the optimal number of periods the leader would want the follower to follow.
Obviously, this extension would require some notational clarification of the
interpretation of the parameter K. In the present setup, K determines the
time till the true value of the innovation is revealed and simultaneously the
time the follower would wait in case that it doesn’t immediately adopt. This
extension will be taken up in future research.
Appendix
Derivation of condition (4)
In order to determine which decision delivers the highest expected payoff, we
compare the three options. The follower is better off never adopting to the
new technology, compared to immediately adopting, if V Fn > V F
a . That is:
K−1∑i=0
δiE[ΠF (1, X)
]+
∞∑i=K
δiE[ΠF (1, X)
]> −C +
K−1∑i=0
δiE[ΠF (1, X)
]+
N−1∑i=K
δiE[ΠF (1, X)
]+
∞∑i=N
δiE[ΠF (2, X)
]C >
δN
1− δ
(E[ΠF (2, X)
]− E
[ΠF (1, X)
])(37)
Accordingly, F is better off to never adopt compared to wait for K periods, iff
V Fn > V F
k . Since∑K−1
i=0 δiE[ΠF (1, X)
]evolves in both terms, this reads as:
∞∑i=K
δiE[Π2 (1, X)
]> p
(−δKC +
N+K−1∑i=K
δiΠ2 (1, xs) +∞∑
i=N+K
δiΠ2 (2, xs)
)
+(1− p)∞∑
i=K
δiΠ2 (1, xf )
32
Since∑∞
i=K δiE[Π2 (1, X)
]=∑∞
i=K δiΠ2 (1, xs) + (1− p)∑∞
i=K δiΠ2 (1, xf ),
this reduces to
δKC >∞∑
i=N+K
δiΠ2 (2, xs)−∞∑
i=N+K
δiΠ2 (1, xs)
C >δN
1− δ
(Π2 (2, xs)−Π2 (1, xs)
)≡ C (38)
Derivation of condition (5)
Given that it is not a best response to never adopt the new e-business tech-
nology, i.e. (4) does not hold, F compares the two options of waiting for K
periods until the quality of the innovation is revealed and of adopting imme-
diately. Accordingly, F prefers to wait, if V 2k > V 2
a , which is
p
(−δKF +
N+K−1∑i=K
δiΠ2 (1, xs) +∞∑
i=N+K
δiΠ2 (2, xs)
)> −F +
∞∑i=N
δiE[Π2 (2, X)
]
+(1− p)∞∑
i=K
δiΠ2 (1, xf ) +N−1∑i=K
δiE[ΠF (1, X)
]
Again, since∑∞
i=K δiE[Π2 (1, X)
]=
∑∞i=K δiΠ2 (1, xs) +
(1− p)∑∞
i=K δiΠ2 (1, xf ), this reduces to
(1− pδK)F +∞∑
i=N+K
p(δiΠ2 (2, xs)− δiΠ2 (1, xs)
)>
∞∑i=N
δiE[Π2 (2, X)−ΠF (1, X)
](1− pδK)F >
δN
1− δE[Π2 (2, X)−ΠF (1, X)
]−δK+N
1− δp(Π2 (2, xs)−Π2 (1, xs)
).
(39)
which is the outcome of (5).
33
Data tables for the calibration excercise
Scenario 1 - Data table
C V Ln V L
k V La V F
n V Fk V F
a
0.00 0.130 0.214 0.277 0.050 0.128 0.1470.05 0.080 0.164 0.227 0.050 0.104 0.0970.10 0.030 0.114 0.177 0.050 0.080 0.0470.15 −0.020 0.064 0.127 0.050 0.056 −0.0030.20 −0.070 0.014 0.077 0.050 0.032 −0.0530.25 −0.120 −0.036 0.027 0.050 0.008 −0.1030.30 −0.170 −0.086 −0.023 0.050 −0.016 −0.1530.35 −0.220 −0.136 −0.073 0.050 −0.040 −0.2030.40 −0.270 −0.186 −0.123 0.050 −0.064 −0.2530.45 −0.320 −0.236 −0.173 0.050 −0.088 −0.3030.50 −0.370 −0.286 −0.223 0.050 −0.112 −0.3530.55 −0.420 −0.336 −0.273 0.050 −0.136 −0.4030.60 −0.470 −0.386 −0.323 0.050 −0.160 −0.453
Table 1: Expected present values with variable C for Q ≥ S ≥ R
Scenario 2 - Data table
C V Ln V L
k V La V F
n V Fk V F
a
0.00 0.130 0.214 0.277 0.050 0.257 0.3630.05 0.080 0.164 0.227 0.051 0.233 0.3130.10 0.030 0.114 0.177 0.052 0.209 0.2630.15 −0.020 0.064 0.127 0.053 0.185 0.2130.20 −0.070 0.014 0.077 0.054 0.161 0.1630.25 −0.120 −0.036 0.027 0.055 0.137 0.1130.30 −0.170 −0.086 −0.023 0.056 0.113 0.0630.35 −0.220 −0.136 −0.073 0.057 0.089 0.0130.40 −0.270 −0.186 −0.123 0.058 0.065 −0.0370.45 −0.320 −0.236 −0.173 0.059 0.041 −0.0870.50 −0.370 −0.286 −0.223 0.060 0.017 −0.1370.55 −0.420 −0.336 −0.273 0.061 −0.007 −0.1870.60 −0.470 −0.386 −0.323 0.062 −0.031 −0.237
Table 2: Expected present values with variable C for S ≥ Q ≥ R
34
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